The present invention comprises a new and distinct cultivar of Floribunda-type rose plant known by the varietal name ‘RNF Purple 01’. The new variety was discovered in April of 2010 in Gifu, Japan. The new variety is the result of a planned breeding program between an unpatented Rosa L. variety named ‘Blue Moon’ (female parent) and an unnamed and unpatented Rosa rugosa variety (male parent) from the breeder's own collection. ‘RNF Purple 01’ differs from its female parent in petal shape and the fact that the new variety has a fragrance, but ‘Blue Moon’ does not. Additionally, ‘RNF Purple 01’ exhibits a similar petal shape and existence of a fragrance to its male parent, but differs from its male parent in its actual fragrance and ‘RNF Purple 01’ has fewer thorns and more leaves. When ‘RNF Purple 01’ is compared to Rosa L. ‘Wish AI’ (currently unpatented in the U.S., Japanese Patent No. 21842), the varieties are similar in that they both exhibit a fragrance, lack eyes on the flowers, and are double-flowering in nature. The new variety differs from ‘Wish AI’ in petal color and shape and also exhibits a stronger fragrance than ‘Wish AI’. When generally compared to other rose varieties known to the breeder, the new variety differs in its strong fragrance, its type of fragrance, and in flower color. ‘RNF Purple 01’ has been trial and field tested and has been found to retain its distinctive characteristics and remain true to type through successive propagations.